Rational Functions Review

Front

What is a rational function?

Back

A rational function is a function that can be expressed as the quotient of two polynomials, where the denominator is not zero.

Front

What is the vertical asymptote of a rational function?

Back

The vertical asymptote is a line that the graph of the function approaches but never touches, determined by the values of x that make the denominator zero.

Front

How do you find the horizontal asymptote of a rational function?

Back

The horizontal asymptote can be found by comparing the degrees of the numerator and denominator polynomials. If the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is y=0. If they are equal, the asymptote is y=ratio of leading coefficients.

Front

What is the process for adding rational expressions?

Back

To add rational expressions, find a common denominator, rewrite each expression with that denominator, and then combine the numerators.

Front

What is the process for subtracting rational expressions?

Back

To subtract rational expressions, find a common denominator, rewrite each expression with that denominator, and then subtract the numerators.

Front

What does it mean to simplify a rational expression?

Back

Simplifying a rational expression means reducing it to its lowest terms by factoring the numerator and denominator and canceling common factors.

Front

What is a slant asymptote?

Back

A slant (or oblique) asymptote occurs when the degree of the numerator is exactly one more than the degree of the denominator, and it can be found using polynomial long division.

Front

What is the significance of the denominator in a rational function?

Back

The denominator determines the domain of the function and the location of vertical asymptotes.

Front

How do you determine the domain of a rational function?

Back

The domain of a rational function includes all real numbers except those that make the denominator equal to zero.

Front

What is the first step in solving a rational equation?

Back

The first step is to identify and eliminate any denominators by multiplying both sides of the equation by the least common denominator (LCD).